Approximation by p-Faber polynomials in the weighted Smirnov class E-P (G,omega) and the Bieberbach polynomials

Abstract

Let G subset of C be a finite domain with a regular Jordan boundary L. In this work, the approximation properties of a p-Faber polynomial series of functions in the weighted Smirnov class EP (G, W) are studied and the rate of polynomial approximation, for f epsilon E-p(G, omega) by the weighted integral modulus of continuity, is estimated. Some application of this result to the uniform convergence of the Bieberbach polynomials rr, in a closed domain (G) over bar with a smooth boundary L is given.